133

10

Effective population size in relation to genetic modification

of Anopheles gambiae sensu stricto

Charles E. Taylor�

and Nicholas C. Manoukis�

Abstract

Effective population size (Ne) is a single number which allows us to relate a large

part of population-genetics theory built around ideal populations to real populations.

In the case of Anopheles gambiae, Ne is important to interpreting the temporal and

spatial distribution of genes. These patterns are in turn used to explore the structure of

(typically non-ideal) natural populations. We discuss the complex structure of An.

gambiae s.s. in and around Banambani, Mali, as it is currently understood, based on

estimates of Ne. This reveals a population that is structured temporally between and

within years, spatially between villages and non-dimensionally into chromosomal

forms. We suggest that the subpopulations of this species might usefully be viewed as

a metapopulation. Successful and efficient genetic modification of An. gambiae will

require as complete an understanding of their population structure as possible, which

we believe can be attained through the convergence of multiple population-genetic

techniques and the application of new methods.

Keywords: effective population size; Ne; Anopheles gambiae; population structure;

Mali

Introduction

The abstract ideal for most theory in population genetics and ecology is a

panmictic population – a single, randomly mating group of individuals in which the

population size stays constant, all offspring have an equal chance to reproduce and

there is no geographic variation in gene or genotype frequencies. Like frictionless

surfaces or perfect vacuums in theoretical physics, the ideal panmictic population

plays an important role in theoretical population genetics, though no such ideal

population actually exists. Rather, all real populations are in some way(s) structured.

That is to say, they consist of subpopulations that are finite in size, may or may not

mate randomly, may or may not share migrants among one another, and probably

change size over time. Making inferences or predictions about these populations

requires that their structure be understood and described in a manner commensurate

with existing theory. The notion of effective population size, Ne, plays an especially

central role for describing this population structure. Ne may be defined to be the size

of an ideal population that exhibits the same rate of drift as the actual population it

�

Department of Organismic Biology, Ecology and Evolution, University of California, Los Angeles,

CA 90095-1606 E-mail: taylor@biology.ucla.edu; manoukis@ucla.edu

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characterizes. As Futuyma (1998) puts it: “if we count 10,000 adults in a population

but only 1,000 of them successfully breed, genetic drift proceeds at the same rate as if

the population size were 1,000, and this is the effective size”. Alternatively, as

discussed later in this chapter, there are huge seasonal differences in the population

size of An. gambiae. The harmonic mean of these sizes is Ne. Ne was introduced by

Sewall Wright, with important subsequent contributions by G. Malécot, J. F. Crow,

M. Kimura and others. See Wright (1969), Crow and Kimura (1970) and Kimura and

Ohta (1971) for useful and accessible discussions.

In this chapter we are concerned with Ne as it can be used to describe and make

inferences about the population structure of Anopheles gambiae s.s., with an emphasis

on its utility for guiding efforts to introduce a genetically modified vector to control

malaria. After a few introductory remarks about taxonomic questions we will describe

the population biology of An. gambiae in one location that has been studied for

several decades. With these components to anchor the discussion we will examine

how Ne and associated parameters of population structure are measured generally, and

their values estimated specifically at our focal location. We then mention some new

theoretical developments that are likely to assist our understanding. Finally, we

conclude with some recommendations about what, in our opinion, are the outstanding

research questions about population structure that must be investigated prior to an

attempt to genetically modify natural Anopheles populations.

The population structure of An. gambiae is quite complex. The highest taxonomic

level in the system is An. gambiae sensu lato (s.l.) that comprises at least 7 species,

one of which is An. gambiae sensu stricto (s.s.). An. gambiae s.s. in turn has as many

as 5 different “chromosomal forms.” In some locations (e.g. Mali), distributions of

chromosomal forms coincide with “molecular forms” which can be distinguished with

polymerase chain reaction (PCR) assays (Favia et al. 1997; 2001). This is not,

however, the case in all locations (Della Torre et al. 2002; 2001). Gene flow across

the forms is limited, so this is an important part of the population structure. For a

comprehensive survey of the chromosomal forms of An. gambiae s.s. see Touré et al.

(1998b), and for a recent description of the population structure around Banambani,

Mali, see Taylor et al. (2001).

Our principal focus in this paper is on Anopheles gambiae s.s. in the village of

Banambani, Mali, and its surrounding area, where three chromosomal forms are

present – termed Bamako, Savanna and Mopti. There are at least three types of

structure that relate to Ne in this area. The first is the extent of population-size changes

over the year and between years. The second is the structure imposed by

chromosomal forms. Finally there is geographic structure because the species inhabits

discrete patches (villages), among which gene flow is limited. A significant

understanding of the complex structure in the study area is critical for the successful

introduction of genetically modified An. gambiae. It is important to know, for

example, how many individuals will need to be released in order to alter the

population, how fast the introduced genetic element will spread from the site of

release and if it will move from one form or species into another. As we will see

below, even simple models for known features of population structure in this species

lead to quite complex patterns of gene flow.

Structure of Anopheles gambiae s.s. at Banambani

Mark-release-recapture (MRR) studies conducted at peak seasonal abundance

during a six-year period indicate that there is much variation in the size of local

Taylor and Manoukis

135

populations of An. gambiae s.s. Annual abundance estimates varied at least 4-fold, as

shown in Table 1, from Taylor et al. (2001). Compounding the variability of

population size between years, the density of An. gambiae s.s. changes dramatically

within a single year. For example, a survey in non-irrigated villages near the Niono

irrigation projects (Dolo et al. 1999) found peak numbers of bites in villages during

the wet season to be more than 1000 times the number recorded during the dry season.

Table 1. Population sizes from 1993 to 1998 estimated from mark-release-recapture

experiments at the village of Banambani, Mali (from Taylor et al. 2001). All measurements

were made at the peak of seasonal abundance (August-September).

Year Replicates Released Recaptured Daily Survival Estimated N

1993 3 938 83 0.80 20,178

1994 4 1,913 57 0.80 64,002

1996 4 1,421 44 0.92 63,006

1997 2 1,002 24 0.97 53,400

1998 4 1,205 21 0.97 79,280

Seasonality seems to vary from place to place; near our study site in Banambani we

have estimated dry-season population sizes to be 5 to 10% of the wet-season peak

(Taylor et al. 2001, Touré, personal communication). Assuming a more or less

exponential growth and decline between the seasonal low and highs, a typical annual

cycle in the An. gambiae s.s. population at Banambani is depicted in Figure 1.

Incidence of the chromosomal forms of An. gambiae s.s. also vary during the year.

All three forms, Bamako, Savanna and Mopti are about equally numerous during the

wet-season peak, in late August to early September, but during the drier part of the

year the Savanna and Bamako forms decrease in numbers, so Mopti individuals

comprise nearly all of the mosquitoes that can be collected then. Based on the data of

Touré et al. (1998b) the numbers of each form are approximately as shown in Figure

2.

The three forms found at each location are thought to exchange genes among

themselves, though how much and the significance of this is still unclear.

Nonetheless, some exchange certainly occurs. The extent of this is further discussed

in Taylor et al. (2001). Based on the number of hybrids observed, the number of

migrants from one form to another is estimated to be in the order of 0 - 11%

depending on the forms exchanging genes and the manner in which gene flow was

estimated (Touré et al. 1998b; Tripet et al. 2001). There is currently insufficient

information to determine whether gene flow is symmetrical or not.

Finally, there appears to be some movement of individuals among villages. Touré

et al. (1998a) and Dolo (2000) report on MRR studies where released females were

captured in neighbouring villages, but the numbers were low and the confidence limits

large. As would be expected, there appears to be less gene exchange among villages

farther apart than among those closely together (Johnson 1969). Carnahan et al.

(2002) collated all of the available microsatellite DNA studies and found a linear

relation between distance and log gene flow (i.e. Log Nem), as expected from

theoretical considerations (see Table 2, below, and Kimura and Ohta 1971). In this

case m is the {number of migrants entering a subpopulation}/{the size of that

subpopulation}. For distances a few kilometres apart, the typical inter-village distance

around Banamabani, m is about 0.008-0.039.

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136

Figure 1. Estimated seasonal change in size of the adult population of Anopheles gambiae s.s.

in Banambani, Mali. The broken line represents the value of Ne, calculated as per equation

(1), below.

Figure 2. Estimated size of the adult populations of each of three chromosomal forms of

Anopheles gambiae s.s. collected in and around Banambani, Mali.

Taylor and Manoukis

137

Putting all this together, the full population structure around Banambani is

summarized in Figure 3, according to the best information available.

Figure 3. Summary of the population structure of the three chromosomal forms around

Banambani, Mali. The series begins in the dry season (March) and proceeds through the

following dry season (February). The population sizes of the three chromosomal forms are

shown as discs, with the area proportional to the size of the population. The discs at each

location represent (from bottom to top): Mopti, Savanna and Bamako forms. Locations in the

map shown hosting populations are those sampled by Touré et al. (1998a). Villages between

them are not shown. All connecting pipes represent gene flow; white is between chromosomal

forms and black is between villages. The diameter of the pipe is proportional to the magnitude

of migration. The time bar in the upper right corner of each frame represents one year from

March to March. The full movie from which these frames were excerpted is available online

at http://taylor0.biology.ucla.edu/~manoukis/Structure.

Measuring population structure

Several methods have been used to measure the principal features of population

structure, population sizes and migration rates. These have been classed as “direct” or

“indirect” by Slatkin (1985), and correspond to “ecological” and “genetic” by Taylor

and Powell (1983). Here we follow Slatkin’s terminology.

Direct measures of population structure consist of those measures of population

properties themselves. For example, several groups have conducted MRR studies of

adult female An. gambiae (see Costantini et al. 1996; Touré et al. 1998a). Relative

density can be estimated from how many bites a sedentary person receives during

fixed periods (Dolo et al. 1999), and larval dippings have been used to estimate

numbers of immatures (Service 1993). Movement and migration are inferred by

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recaptures from distances or villages away from a release site and interbreeding

between forms by the numbers of hybrids that can be detected. Service (1993) has an

extended discussion about application of these methods for mosquitoes; more general

discussions of these topics can be found in Blower, Cook and Bishop (1981), Johnson

(1969) and Turchin (1998).

Indirect measures of population structure are the methods of primary interest here.

A particular history of size change and gene flow should give rise to corresponding

patterns of allele frequencies in space and/or time. If those patterns can be

appropriately measured, then it is frequently possible to work backwards and infer the

population structure that gave rise to the pattern. Some population-genetic patterns

that have been measured to infer the structure and history of populations are shown in

Table 2.

Exact specification of the models and precise definitions of the variables is not

possible here; the references given should be consulted for these. Very briefly, ne

refers to effective number of alleles and � is a measure of genetic diversity derived

from allele frequencies by Watterson (1975), often used in coalescent theory. These

both depend on the product of effective population size and neutral mutation rate, �.

There are several models of gene flow that have received theoretical attention; these

differ about the importance of long-distance (m or m�), or short-distance (m1)

migration and whether there are discrete populations of size Ne or if they are

distributed with a constant density. Distance, whether continuous (x) or discrete

population steps (�), affects how correlated are populations to one another. FST is a

correlation of allele frequencies across subpopulations, closely related to r(�) and

�(x). (Ne is defined for these measures and could be incorporated into the equations,

but we have chosen to leave them in their more traditional forms.) Because large

populations are expected to drift more than small populations, change in allele

frequency (p) from generation to generation, measured by �2(p), will depend on

effective population size. And finally, when gene trees are constructed, the time, t, to

the most recent common ancestor, MRCA, will depend on effective population size

and mutation rate.

Table 2. Some indirect methods used to study patterns of genetic variation. Key: HC = Hartl

and Clark (1997); H = Hudson (1990); FL = Fu and Li (1999); CK = Crow and Kimura

(1970); KO = Kimura and Ohta (1971); A = Anderson, Williamson and Thompson (2000); W

= Waples (1989).

Measure Formulae Reference

1. Amount of polymorphism 14Nn ee �� �HC

�� eN4�H; FL

2. Differentiation of populations CK; KO

Island model 1)m1/(4NF eST ��KO

Isolation-by-distance model��� ]/) x(2Exp[-(x) 1/2

�

KO

Stepping-stone model��� ]/)/m(4mExp[-)r( 1/2

1�

�

KO

3. Temporal changes in allele

frequency)]1/2N-(1-[1p)-p(1(p) e

2��

A; W

4. Coalescence mNt(MRCA) e�H; FL

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139

Patterns of detectible genetic variation shown in Table 2 are all sensitive to the

structure and history of the population being studied. Taken together with estimates of

Ne, these provide insight into how populations of An. gambiae are structured, though

there may be more than one interpretation for any particular pattern.

Estimating Ne

In the equations in Table 2 the estimates of effective population size can be taken

as similar to the actual population size, N, but because of the extensive structure

already discussed, N is likely to be a poor approximation of the effective population

size. Recall from above that Ne is defined to be the size of an ideal population that

exhibits the same rate of drift as the actual population (Crow and Kimura 1970). Such

drift might affect inbreeding, variance in gene frequencies, or rate of extinction of

alleles. Consequently, one can distinguish inbreeding-effective population size,

variance-effective population size, and eigenvalue-effective population size or

extinction-effective population size (Crow 1956). In most cases these will be similar

to one another and no distinction need be made, but in some instances they can differ

substantially (see Kimura and Ohta 1971).

Figure 1 illustrates how an ideal population may drift at the same rate as the

average drift of an actual population. When the population size is low, as at the

beginning and end, then the allele frequencies will drift rapidly, but when the

population size is large, then the drift will be slower. Between these extremes there

must be an average rate that can be calculated by noting that the rate of drift at time t

is proportional to 1/Nt. The average rate of drift, described by 1/Ne, is seen to be:

(1/Ne) = (1/k) (1/N1 + 1/N2 + … +1/Nk) (1)

Other adjustments can be made for other departures from the idealized, panmictic,

population. For example when there are Nm males and Nf females then asymmetrical

contributions to the next generation can be adjusted by:

Ne = (4 Nm Nf ) /(Nm + Nf) (2)

How important unequal sex ratios are for Anopheles is, at present, unknown. We

do not know how many males actually mate and this number might be highly skewed.

A third type of adjustment, for non-Poisson survival of offspring, is

Ne = (4N – 2)/(Vk + 2) (3)

where Vk is the variance in numbers of offspring per parental pair. When survival of

each egg has a Poisson distribution with mean 2, then Vk = 2. The true variance is

probably much greater. Consider a common larval site for Anopheles, puddles.

Survival of all the eggs laid there is hit or miss, in large part dependent on whether the

puddle dries up or is washed away. Assuming that each female lays several eggs when

she oviposits, then some few females who lay in fortunate sites will produce more

offspring than others, thereby increasing Vk and decreasing Ne.

Note that these equations all refer to discrete generations, an idealization that is not

really appropriate for An. gambiae. It is possible to make adjustments when a stable

age distribution can be inferred, but a rough approximation – that Ne is roughly the

number of mosquitoes born during some time interval that make it to the age of

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140

reproduction times the number of time intervals during which they reproduce – is

more practical. In general multiple considerations to correct N so it approaches Ne can

be combined with one another, simply by taking a composite function (Kimura and

Ohta 1971).

Anopheles gambiae s.s. and metapopulations

Combining the information above we get the following picture of genetic structure

on Anopheles gambiae s.s. at our focal research site, Banambani village, Mali (Table

3). The calculations and rationale are described in Taylor et al. (1993) and Lanzaro et

al. (1998).

Table 3. Estimates of effective population size presented in relation to some of the structure in

An. gambiae around Banambani, Mali. In this table the total effective population size is a bit

larger than the sum of those for the forms it comprises. This is because of rounding error and

because there are some unassigned or hybrid individuals.

Parameter Notation Value (Banambani, Mali)

Effective population size Ne,tot 4,400

Ne,Bam 900

Ne,Sav 1,500

Ne,Mop 1,900

Migration to adjacent population mss 0.008

Gene flow among forms NemBS 16

NemSM 12

NemBM 2

The figures in Table 3 vary in their reliability, particularly the numbers and

migration rates when population sizes are small during the dry season. Frankham,

Ballou and Briscoe (2002) report that an average ratio of Ne/N across many species is

approximately 0.1, not far off from the ratio estimated from Tables 1 and 3. There is

little allowance here for year-to-year variation, which we know to be substantial in

our study area (Table 1). In addition to temporal structure, the population of this

species around Banambani is structured spatially (between villages) and non-

dimensionally (non-random mating due to chromosomal forms), in the terminology of

Taylor and Powell (1983). This degree of complexity is hard to capture and quantify

even with multiple patterns of genetic variation.

A new development in ecological genetics – metapopulation analysis – holds much

promise for furthering our understanding of structure in this species. A

metapopulation is a set of local populations, many of which may be unable to sustain

themselves, where local extinction may be frequent, but where migration and

recolonization can retain a dynamic equilibrium.

Several types of metapopulations can be distinguished (see Hanski and Gilpin

1997). Three of these have particular significance for the introduction of genetically

modified An. gambiae: (1) The 'classical' metapopulation of Levins (1969), a network

of equivalent local populations that inhabit discrete patches. The probability of

extinction is equal for all patches, as is the probability of recolonization and origin of

migrants. (2) A mainland-island metapopulation, a system of habitat patches which

are within dispersal distance of a very large (mainland) patch which never suffers

extinction. (3) A source-sink metapopulation, where some patches have a negative

growth rate (sinks) and are maintained by migration from patches with a positive

Taylor and Manoukis

141

growth rate (sources). Which patches are sources or sinks may vary seasonally or

otherwise.

Describing the metapopulation of An. gambiae around Banambani as one of these

types or as an intermediate will require careful application of direct and indirect

methods of assessing structure. Genetic data can be used to test particular hypotheses

about structure and type as an extensive body of theory now exists that describes how

the patterns of gene frequencies and molecular evolution are determined by

metapopulation structure. A better description of the importance of drift for the

population can be attained by examining this type of question. Detailed discussion of

these is beyond the scope of this work, but the reader is referred to Pannell and

Charlesworth (2000), Gavrilets, Acton and Gravner (2000), Whitlock (1999) and

Slatkin (1977) for good examples of the utility of metapopulation theory.

We have used computer simulation to explore how a transposable element might

move through a classical metapopulation under very simple conditions. The outcome

of one such simulation is shown in Figure 4, for a transposable element released at a

frequency of 0.1 in the Mopti population of one village in March. This hypothetical

transposable element is associated with a single gene which induces 100%

refractoriness to Plasmodium. We assume that there is no dissociation of the

transposable element and the gene of interest. In addition, the transposable element

has a fixed level of meiotic drive so that heterozygotes would contribute 2p(1-p)(1+i)

of the modified gene rather than the 2p(1-p) of Mendelian segregation. We took i=

0.75 for these simulations. We assumed that it had no negative fitness effect on the

carrier. These conditions are oversimplified (Boëte and Koella 2002), but our purpose

here is to explore the effect of structure on the movement of an ideal transposable

element and gene for malaria refractoriness. The incorporation of more realistic

transposable-element dynamics to this simulation is a future goal.

The status of the population at two-month intervals for two years is illustrated. The

degree of red coloration in the figure shows what proportion of the population is

carrying the transposable element. It is evident that incorporation of the transposable

element is far from simple and depends critically on the population structure.

With the prospect of introducing a transposable element into the population, it is

critical to understand more about the equivalency, permanence and demographic

synchrony of patches. The results attained this far go part of the way to describing

important characteristics of the metapopulation. The mathematical analyses and

computer simulations made to date are still only rough. Much more detail, especially

with regard to population properties during the dry season, contributions from

different locations where immatures develop and more information on mating

behaviour are desirable to attain a level of resolution that will make modelling of the

effect of such a transposable element effective and any introduction successful.

Conclusion and recommendations

Estimates of effective population size are of little intrinsic interest by themselves.

This is particularly evident when we consider genetic-modification schemes like the

release of a transposable element into the metapopulation. In these circumstances

neutrality cannot be assumed, so random genetic drift, to which Ne refers, is largely

irrelevant to incorporation of the transforming genes. Rather, the importance of Ne lies

in its utility to probe the structure of the population by allowing us to relate observed

patterns of allele frequencies to particular aspects of population structure, which we

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142

Figure 4. Simulated movement and frequency change of a transposable element through a

metapopulation of Anopheles gambiae s.s. around Banambani, Mali. The release consists of

0.1 of the Mopti population in Banambani in March. Symbolic representations of the

structured population are as in Figure 3, with the addition of red coloration to depict the

proportion of the population which possesses the transposable element. The full movie from

which these frames were excerpted is available at:

http://taylor0.biology.ucla.edu/~manoukis/Structure.

have seen is very relevant for determining the pattern of transformation. In this area,

the estimation of Ne will remain critical and of enormous utility.

It is not known if genetic modification will proceed through the use of transposable

elements or if malaria control will be accomplished through other methods. It may, for

example, happen that sufficiently variable refractory mosquitoes can-not be made,

that the genetic changes can-not be effected into natural populations or that ethical

considerations will preclude usage of this method. Our research agenda should be

constructed so that information acquired by our efforts will benefit malaria control by

any means – such as bed nets, a vaccine, anti-malarial drugs or new insecticides.

Both direct and indirect measures of gene flow will be necessary for estimates of

population structure. They each give somewhat different information because they are

based on different assumptions (Slatkin 1987). Direct methods are necessarily bound

Taylor and Manoukis

143

by space and time and have low sensitivity, which is to say they are not well suited to

detecting rare events. On the other hand, recorded events are real and may give insight

into yearly cycles or median conditions, given enough observations. Indirect methods

typically assume complete neutrality and equilibrium conditions, and typically give

results that are open to multiple interpretations. The use of both approaches helps to

fill in the gaps left by the assumptions of one method or another, making estimates

more robust. Especially in the case of rare events, which are of enormous importance

to the prospects of genetic modification of An. gambiae, multiple sorts of evidence

increase our confidence in the estimates.

In terms of population structure, the issues most in need of clarification are:

� Establish metapopulation structure of An. gambiae. In particular, determine if all

patches are equivalent, if there are sources/sinks and especially what, if any, is the

extirpation regime.

� Better estimates of gene flow and population size are needed so Ne can be used in

estimating the importance of rare events.

� Examine in detail the nature and extent of gene flow between chromosomal forms

in other parts of Africa.

� Extend research to other sites around the continent, especially east and central

Africa. There is no reason to believe that what is true for the species in one area

will also pertain to another.

� Identify and then survey in great depth island populations of An. gambiae that are

serious candidates genetic-control trials.

One of the most urgent needs, in our opinion, is to establish the metapopulation

structure of An. gambiae by directly measuring and indirectly inferring parameters

that are of importance to determining metapopulation characteristics, such as

synchrony, extirpation regime and patch equivalency. One important area here is to

examine the extinction regime of the populations in the villages, which may be

undertaken by both direct and indirect methods.

Improvement of existing estimates of hybridization, migration and population size

during the wet season is also necessary for a more comprehensive characterization of

the system. A promising avenue for improving some of these is revealed by the

continuing development of coalescence theory, which may be described as an

examination of genealogical patterns of genes in time. These powerful methods

should enable researchers to efficiently probe fine-grained details and variation of the

population.

This sort of investigation would be most useful if extended to other sites. In

addition to the power of comparative studies that would be gained, some sense of the

limits of variability in system dynamics could also be explored. Such an

understanding will ultimately prove critical in predicting how a given system might

change when faced with attempts at genetic manipulation or externally varying

conditions, like changes in climate or increasing human development, for example.

Once we have a more complete quantification of the factors we already know are

important to the structure of the species, realistic modelling of the effects of genetic

modification of An. gambiae will be possible. The more complete our understanding

of the system is as a metapopulation the more useful and accurate the modelling

efforts can be.

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144

Acknowledgments

This work has been supported by grants from NIH. We are indebted to Mario

Coluzzi, Greg Lanzaro, Guimogo Dolo and Yeya T. Touré for help in formulating the

ideas presented here. We also thank Joan Slottow, Maria Diuk-Wasser and Sigrid

Rian for help preparing the illustrations presented in Figures 3 and 4, and Phil

Lounibos for his many helpful suggestions on presentation.

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